Int. J. Open Problems Compt. Math., Vol. 3, No. 3, September 2010 ISSN 1998-6262; Copyright © ICSRS Publication, 2010 www.i-csrs.org Lacunary Interpolation by Quartic Splines with Application to Quadratures Abbas Y. Al Bayati, Rostam K. Saeed and Faraidun K. Hama-Salh Faculty of Numerical Optimization, University of Mosul, Iraq, e-mail: profabbasalbayati@yahoo.com Faculty of Numerical Analysis, Salahaddin University/Erbil, Iraq, e-mail: rostamkarim@yahoo.com Faculty of Numerical Analysis, University of Sulaimani, Iraq. e-mail: faraidun@yahoo.com Abstract The aim of this work is to construct lacunary interpolation based on quartic C 3 -spline and to apply this spline function for finding approximate values of smooth function and its continuous derivatives. Upper bounds for errors and convergence analysis of the presented lacunary interpolation studied. Also, we have solved numerically two examples, to show the validity of the prescribed method by depending on the L∞-error estimation. Keywords: Lacunary interpolation model, Convergence analysis, Spline function, Quadrature, Algorithm. AMS subject classifications: 65D05, 65D07 and 65D32. 1 Introduction In this paper, we apply quartic C 3 -spline interpolation to develop a numerical method for obtaining approximations to the value of integration, finding the error bounds and suitable assumptions with applications showed that this spline exists and is unique. The convergence analysis and the stability of the approximate solution is investigated and compared with the exact solution to illustrate practical usefulness of our approximation. El-Tarazi and Sallam (1987) and (1993) have constructed a quasi-Hermite interpolatory by quartic spline with periodic second